Related papers: A-priori Estimates and Existence for Quantum Gibbs…
We discuss the properties of two open quantum systems with a general class of irreversible quantum dynamics. First we study Lieb-Robinson bounds in a quantum lattice systems. The time-dependent generator of the dynamics of the system is of…
We use a Hamiltonian dynamics to discuss the statistical mechanics of long-lasting quasi-stationary states particularly relevant for long-range interacting systems. Despite the presence of an anomalous single-particle velocity distribution,…
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…
Collective spin systems -- spin ensembles coupled to a common reservoir and effectively described by a single macrospin -- play an important role in both atomic and solid-state physics. Their intrinsic nonlinearity gives rise to multiple…
We discuss the existence and nonexistence of solutions to the steady-state Gierer-Meinhardt system $$ \begin{cases} \displaystyle -\Delta u=\frac{u^p}{v^q}+\lambda \rho(x) \,, u>0 &\quad\mbox{ in }\mathbb{R}^N\setminus K,\\[0.1in]…
We present a novel quantum algorithm for estimating Gibbs partition functions in sublinear time with respect to the logarithm of the size of the state space. This is the first speed-up of this type to be obtained over the seminal…
We discuss a Statistical Mechanics approach in the manner of Edwards to the ``inherent states'' (defined as the stable configurations in the potential energy landscape) of glassy systems and granular materials. We show that at stationarity…
The functional-integral quantization of non-Abelian gauge theories is affected by the Gribov problem at non-perturbative level: the requirement of preserving the supplementary conditions under gauge transformations leads to a non-linear…
Lattice gauge theory has provided a crucial non-perturbative method in studying canonical models in high-energy physics such as quantum chromodynamics. Among other models of lattice gauge theory, the lattice gauge-Higgs model is a quite…
Continuum limits are a powerful tool in the study of many-body systems, yet their validity is often unclear when long-range interactions are present. In this work, we rigorously address this issue and put forth an exact representation of…
Quantum theory is indeterministic, but not completely so. When a system is in a pure state there are properties it possesses with certainty, known as actual properties. The actual properties of a quantum system (in a pure state) fully…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and…
The quantum systems with finite-dimensional Hilbert space have several applications and are intensively explored theoretically and experimentally. The mathematical description of these systems follows the analogy with the usual…
We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…
This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…
After many years of development of the basic tools, quantum simulation with ultracold atoms has now reached the level of maturity where it can be used to investigate complex quantum processes. Planning of new experiments and upgrading…
A generalization of the Gibbs entropy postulate is proposed based on the BBGKY hierarchy as the nonequilibrium entropy for a system of N interacting particles. This entropy satisfies the basic principles of thermodynamics in the sense that…
We report on the utility of using Shannons Sampling theorem to solve Quantum Mechanical systems. We show that by extending the logic of Shannons interpolation theorem we can define a Universal Lattice Basis, which has superior interpolating…
The preparation of Gibbs thermal states is an important task in quantum computation with applications in quantum simulation, quantum optimization, and quantum machine learning. However, many algorithms for preparing Gibbs states rely on…